1. Jie Shan (a), Feng Wang (b), Ernst Knoesel (c), Mischa Bonn (d) Jie Shan (a), Feng Wang (b), Ernst Knoesel (c), Mischa Bonn (d), and Tony F. Heinz (b)Tony F. Heinz (b) (a) Case Western Reserve University (b) Columbia University (c) Rowan University (d) University of Leiden/AMOFL Research supported by NSF Conductivity in Photo-Excited Insulators Probed by THz Time-Domain Spectroscopy

2. Relevant Published Papers E. Knoesel, M. Bonn, J. Shan, and T. F. Heinz, “Charge Transport and Carrier Dynamics in Liquids Probed by THz Time-Domain Spectroscopy,” Phys. Rev. Lett. 86, 340 (2001).E. KnoeselCharge Transport and Carrier Dynamics in Liquids Probed by THz Time-Domain Spectroscopy E. Knoesel, M. Bonn, J. Shan, F. Wang, and T. F. Heinz, “Transient Conductivity of Solvated Electrons in Hexane Investigated with Time- Domain THz Spectroscopy,” J. Chem. Phys 121, 394 (2004).E. KnoeselTransient Conductivity of Solvated Electrons in Hexane Investigated with Time- Domain THz Spectroscopy J. Shan, F. Wang, E. Knoesel, M. Bonn, and T. F. Heinz, “Measurement of the Frequency-Dependent Conductivity of Sapphire,” Phys. Rev. Lett. 90, 247401 (2003).E. KnoeselMeasurement of the Frequency-Dependent Conductivity of Sapphire F. Wang, J. Shan, E. Knoesel, M. Bonn, and T.F. Heinz, “Electronic Charge Transport in Sapphire Studied by Optical-Pump/THz-Probe Spectroscopy,” SPIE Proceedings (in press).E. Knoesel E. Hendry, F. Wang, J. Shan, T. F. Heinz, and M. Bonn, “Electron Transport in TiO2 Probed by THz Time-Domain Spectroscopy,” Phys. Rev. B 69, 081101 (2004).Electron Transport in TiO2 Probed by THz Time-Domain Spectroscopy

3. Charge Transport in Insulators Electrical breakdown Optical breakdown  laser micromachining Basis of radiation detectors This study: prototype crystalline and amorphous material Sapphire (Al 2 O 3 ), MgO:Liquid n-hexane (Bandgap 9-5 eV)(Ionization potential 8.6 eV) Fundamentals of electrons and their transport Polaron = electron + virtual phonon cloud

4. Difficulties in Probing Insulators -Very low intrinsic conductivity -Problems with contacts -Short carrier lifetime  Optical pump/THz probe spectroscopy Also powerful technique for semiconductors, superconductors, …

5.        Optical pump THz Probe Sample Detector Probing Transient Conductivity by THz Time-Domain Spectroscopy E(t)  E(t)X100 Current (j=  E) radiates Conductivity

6. Experimental Setup - Emitter Detector Ti:S Regen 1 KHz, 1 mJ 150 fs, 810 nm Lock-in amplifier Sample Tripling UV: 270 nm 40  J

7. Inject electrons with fs UV pulses Probe with pulsed THz at a variable delay Charge Transport in Liquids Energy (eV) Distance 2 nm 0 0 -8.6 ~ ~ e-e- e-e- Localized bound states Quasi-free state

8. THz E-field and Pump Induced Changes in n-Hexane -0.5 0.0 0.5 1.0 E(t) [kV/cm] 76543210 Time [ps] E(t) 6x10 -3 4 2 0 -2 -4  E(t) [kV/cm]  E(t) Measured THz waveform with and without uv pump radiation. Delay time between UV-pump and THz-probe:  = 67 ps. Knoesel et al. PRL 86, 340 (2001)

9. Electronic Conductivity in n-Hexane 1.21.00.80.60.4 [THz] 2 1 0 -2  ' ;  " [x 10 -3 ]  "  (n e ) quasi-free = 10 13 - 10 15 cm -3  o = (270  50 fs) -1 Data Drude model  p 2 = n e e 2 /(e o m*) - Plasma frequency  0 - Scattering rate  f = e/(m*  o ) =470 cm 2 V -1 s -1

10. Comparison with Complementary Measurement 1 N. Gee. Chem. Phys. 89 (1988) 3710; R. C. Munoz, J. Phys. Chem. 91 (1987) 4639 2 Y. A. Berlin, J. Chem. Phys. 69 (1978) 2401; 3 Mozumder, Chem. Phys. Lett. 233 (1995) 167. Radiolysis studies 1 : + + + + + + + + + - - - - - - - - - X-ray, e - e-e- M+M+ time current hexane  = 0.074 cm 2 V -1 s -1 (average) Electron Mobility  o = (270  50 fs) -1 m*=m 0  f = e/(m*  o ) =470 cm 2 V -1 s -1 THz TDS: Two-state model of solvated electrons 2,3  f = 30 - 300 cm 2 V -1 s -1

11. Dynamics of Quasi-Free Electrons Fluence = 0.3J/cm 2 Decay 360 ps 6 5 4 3 2 1 0 nene [a.u.] 8006004002000 Delay time (ps) ½ fluence Decay > 1 ns 20 3 4 n e [a. u.] 3.503.403.303.20 1000/T [T in K] E a ~ 150 meV Arrhenius fit: e - E a /kT Electron trap binding energy E a - > Non-geminate recombination mechanism

12. Charge Transport in Sapphire 8.9 eV EVEV e h EcEc 4.6 eV +++++ ----- Important optical and electonic material High quality samples available Model ionic material with polaronic effects

13. Polarons & Polaronic Charge Transport New quasi-particle with m* > m band Model widely studied Landau, Froehlich, Lee, Pines, Feynman Specific predictions for transport properties of polarons, but verified only in a limited class of materials. Electrons in crystal are dressed by interaction with optical phonons in strongly polar crystals

14. Drude Model fit: Scattering rate: γ 0 = ( 95 fs ) -1 Mobility: μ e =e/(m * γ 0 )= 610 cm 2 /V-s (m * ≈ 0.27 m 0 ) Electron Scattering Rate and Mobility in Sapphire at Room Temperature

15. Relation between conductivity and dielectric function

16. Drude Model fit: Scattering rate: γ 0 = ( 95 fs ) -1 Mobility: μ e =e/(m * γ 0 )= 610 cm 2 /V-s (m * ≈ 0.27 m 0 ) Electron Scattering Rate and Mobility in Sapphire at Room Temperature

17. Temperature Dependence of Scattering Rate in High Purity Sapphire μ e = 610 cm 2 /V-s μ e = 30,000 cm 2 /V-s

18. Acoustic phonon scattering Optical phonon scattering (polaron theory) Impurity scattering Scattering Mechanism of Electrons in Sapphire ~ ~

19. Temp. dependence Known parameters Unknown parameters  acoustic a T 3/2 c ii : elastic constant  d : deformation potential m * : effective mass  optical b exp (-E/kT)  LO : optical phonon frequency (c) U e-p : electron-optical phonon coupling constant (c) m * : effective mass a. J. Bardeen and W. Shockley, Phys. Rev. 80, 72 (1950) b. F.E. Low and D. Pines, Phys. Rev. 98, 414 (1955) c. M. Schubert, T.E. Tiwald and C.M. Herzinger, Phys. Rev. B. 61(12), 8187 (2000) A Closer Look at the Theory

20. Temperature Dependence of Scattering Rate in High Purity Sapphire Acoustic phonon scattering ~ LO-phonon ~ m * = 0.3 m 0  def = 19 eV

21. Impurity Scattering in Sapphire Ionic impurities High purity

22. ModelElectron band mass (m 0 ) Effective mass (polaron) (m 0 ) Deformation potential (eV) Pines & Low 1 0.250.3019 Garcia-Moliner 2 0.380.4814 Osaca 3 0.650.928.3 1.F. E. Low and D. Pines, Phys. Rev. 98, 414 (1955). 2.F. Garcia-Moliner, Phys. Rev. 130, 2290 (1963). 3.Y. Osaca, Progr. Theoret. Phys. 25, 517 (1961). 4.Y. N Xu and W.Y. Ching, Phys. Rev. B 43, 4461 (1991). 5.J. C. Boettger, Phys. Rev. B 55, 750 (1997). Interpretations Based on Various Polaron Models Numerical simulations Electron band mass 4 : 0.3 - 0.4 m 0 Deformation potential 5 : 19 - 20 eV

23. Fluence = 0.3J/cm 2 Decay 360 ps 6 5 4 3 2 1 0 nene [a.u.] 8006004002000 Delay time (ps) ½ fluence Decay > 1 ns  Non-geminate recombination Fluence Dependence of Carrier Lifetime in n-Hexane

24. Fluence Dependence of Carrier Lifetime in Sapphire -200204060 0.0 0.5 1.0 Signal (a.u.) Time (ps) 0.4 0.3 0.5 0.2 0.1 Fluence (mJ/cm 2 )

25. Carrier Lifetime in Sapphire Observations: Large deviation from sample to sample (sensitive to impurities, defects) Temperature dependence of carrier lifetime deviates from sample to sample High purity sapphire wafer Sapphire window

26. Summary THz Time-Domain Spectroscopy: Measure complex conductivity over broad far-IR spectral range THz probing of electronic charge transport: +Determine basic transport parameters: carrier density, scattering rate +Doesn’t require contacts... Together with ultrafast excitation +Access nonequilibrium systems and their dynamics +Probe materials without intrinsic conductivity, short-lived carriers Investigated charge transport in model non-polar liquids (hexane) and model wide-gap insulators (sapphire) Demonstrated high carrier mobilities Determined carrier lifetimes and trapping mechanisms Analyzed scattering mechanism from T-dependent conductivity